Catadioptric reflex reflecting lens



Feb. 2l, 1950 R W, JOHNSON 2,498,426

CATADIOPTRIC REFLEX REFLECTING LENS- Filed March 24, 1947 53 INVENTOR.

ROY' w..1oH-soN 57 58 ATTORNEYS Patented Feb. 21, 1950 UNITED STATES PATENT OFFICE CATADIOPTRIC REFLEX REFLECTING LENS Roy W. Johnson, Detroit, Mich.

Application March 24, 1947, Serial No. 736,666

11 Claims. (Cl. 8882) f The present invention relates to a reflecting lens 4and more particularly to a catadioptric lens effective to return an incident light ray after double refraction and reflection along a path substantially parallel to the incident ray.

It is an object of the present invention to provde a catadioptric reflex reflecting lens characterized by the provision of a concave refracting surface at its front face cooperating with one or 'more reflecting systems approximating tetrahedral corners.

' `More specifically, it is an object of the present invention to provide a catadioptric reiiex reflecting lens having a concave refracting surface at its front face and a reflecting system composed of six reflecting surfaces arranged in groups of three each, each group of which approximates a tetrahedral corner.

Other objects and features of the invention will become apparent as the description proceeds, especially when consideredin conjunction with the accompanying drawings, wherein:

Figure 1 is a plan view of the lens;

Figure 2 is a section on the line 2-2 of Figure 1;

Figure 3 is a longitudinal section of a press and die elements for forming the lens;

Figure 4 is a fragmentary section on the line 4-4 of Figure 3;

Figure 5 is an end elevation of the die elements assembled in the press; and

Figure 6 is a diagrammatic View showing the cross sectional shape of a lens constructed in accordance with the present invention, the cross sectional shape corresponding to the sectional view of Figure 5.

Referring now to Figures 1 and 2, the lens I0 is illustrated as of generally circular formation having an attaching flange II, an annular flat center portion I2, a forwardly projecting, conl thedrawings, the axes of symmetry of the tetrahedral corners, which pass through the intersection point of their surfaces, are parallel to each other. l p

'f The preciseshape of the surfaces is best understood by reference to Figure 6. In this figure the reflecting surface I1 is actually a portion of a spherical surface which is tangent to a plane 25 at a point 26. Two other imaginary plane surfaces, each of which is perpendicular to the imaginary surface 25 and to the other plane surface, intersect along a straight line 21 and the reflecting surfaces I5 and I6 are tangent to these last mentioned plane surfaces, the point of tangency being the point 26 previously defined. The radius of curvature of the spherical surfaces I8, I9 and20 is relatively large so that in the portions of these surfaces appearing in the lens the surfaces do not deviate substantially from a plane surface. However,.the optical effect of the deviation from the plane surface is very important and the radius of curvature of the spherical surfaces is related to the curvature of the concave refracting surfaces I4 so as to give a maximum reflex refiecting action of incident rays throughout a wide angle of incidence. Attention is directed to the fact that the spherical reecting surfaces I5 to 20 are concavely presented to the incident ray.

The concave refracting surface I4 approximates a hyperbola but is modified therefrom so that the portions away from the center or axis thereof lie outside of an imaginary hyperbola whose trace is indicated at the dotted line 3D. In other words, the curvature of the refracting surface I4 follows closely an imaginary hyperbola at its central portion but approaching its periphery the curvature of the refracting portion I4 is of increasingly longer radius or of increasingly less curvature.

The optical shape of the concave refracting surface I4 is such that parallel rays of light impinging upon it in a direction parallel with the center line of the optical system are refracted in substantially conical formation and the spherical radius used to describe the grouped reecting surfaces, such as I8, I9 and 20 are so disposed and determined as to return the rays toward the refracting surface I4 in substantially the same conical formation.

Referring to Figure 1, it will be observed that the six reflecting surfaces I5 to 20 inclusive together occupy a generally quadrilateral area having corners of and 120. This area is located symmetrically with respect to the concave refracting surface I4 so that the axis thereof is coplanar with and midway between the axes of symmetry of said tetrahedral corners. Figures 1 to 6 illustrate a preferred form of the lens, in which the major diagonal of the quadrilateral area is slightly longer than the diameter of the concave refracting surface I4 and the minor diagonal (represented by the line 2I in Figure 1) is somewhat shorter than the diameter of the concave refracting surface I4. It is to be understood, however, that these proportions may be altered by practical requirements affecting the thickness of the at portion I2 without in any Way affecting the scope of this invention. In any case, however., the diameter of the refracting surface should be greater than the distance rbetween the axes of symmetry of the tetrahedral corners.

Specifically, a preferred embodiment of the present invention comprises a lens whose outside diameter is 2% inches. The radius of curvature of the spherical surfaces I5 through 2t is 5.884 inches. As previously stated, these spherical surfaces are tangent at the apex of an imaginary tetrahedral corner at the point 26. The concave refracting lens, which as previously sta-ted approximates a hyperbola, has a curvature repre- 'sented by the following table, in which the X dimension is along the axis of the lens and the Y `:dimension is in the direction perpendicular The actual operation of the lens may be under- !sto'od by reference to Figure Y6 which shows light rays 6I and 52 'entering and leaving the lens parallel with the center line 'of its optical system, -"and light rays 53 and 64 entering `and leaving the lens at a wide `angle to the center yline of its optical system. Such rays as 62 and t4, for example, `are first retracted by concave 'surface 4"I4 following which 'they are reflected from 'all lthree of 'the Asurfaces I5, 'I6 and Vi, or IB, IS!

'and '20, and finally are refracted again by surface I4 upon leaving 'the lens.

Rays f63 and 64 illustrate the ability of the lens to reflect rays at wider angles of incidence than is possible with other types of lenses which employ tetrahe'dral reflectors -or vapproximate tetrahedral reflectors. In Eother lenses the reflecting surfaces 'correspondingto surfaces Il' and 20 are so -positioned that wide angled rays impinging upon vthem exceed the limits of total internal reflection and are therebycaused `to pass through the lens instead of being reflected and returned in the fdirection from which they came. Ray 64 in rlfigure vr6 :shows `that `surface 29, and surface I'I in the opposite sense, 'are juxtaposed .in relation to concave surface I4 in such a manner that refraction at the ysaid surface I4 tends to Vmaintain the lrays in total reflecting relation t0 surfaces 2U and II over :a kwide angle of incidence.

'It has been found that this lens may conveniently be formed ina pressing operation when the lens is :formed yof a material such as methyl methacrylate, which is widely known under its trade name Lucita Aiconve'nient method fof producing these lenses with high precision and with ease and economy of manufacture is illustrated in Figures 3 to 5. In these figures a recessed die 35 is provided with die surfaces 3B conforming to the front surface of the lens, including a conical portion 3'I which forms the conical surface I3 of the lens. A pin 38 whose upper surface 39 has been carefully machined to the desired curvature of the concave refracting surface I4 is mounted in the die. The upper die portion comprises a plate 40 having die surfaces 4I 'shaped to cooperate with correspondingly formed portions of the die 35 to form the flange I I. The plate 4U is provided with an opening 42 ylocated centrally therein and received within the opening 42 is a cup 43 having an' internal chamber 44 accurately fashioned to have the hexagonalshape illustrated best in Figure 4. Five pins 5D, 5I, 52,53 and 54 are provided, these pins having their end surfaces ground to the appropriate shape to form the reflecting surfaces I5, I5, I1, I8, I9 and 20. Pins 50, 5I, 53 and 54 each include a concave spherical portion 55 and a fiat portion 56. The central pin 52 is provided at opposite sides with identical concave spherical surfaces 51 and 58, these surfaces meeting `to define the line 59 which reproduces the line 2| in the lens previously defined. It will be observed that each of `the pins 5l) to 54 are of diamond shaped cross `section `having 'acute angles of 60 and obtuse angles of 120, and intert to ll the hexagonal chamber 44.

All of the `'pins 50 to 54 may conveniently be yground with their ends in 4contact at lthe proper angle to a spherical grinding element and assembled vin the relationship illustrated to form a very accurate die whose accuracy is fully reproduced in the finished product.

While the specic dimensions of a preferred embodiment of the present reflex reflecting lens have been given, it will be understood that this is merely an lexample and that of course dimensions of the lens may be modified .as desired so long as the optical relationship and cooperation of refracting and `reflecting surfaces are not changed. It will further be understood that while specific dimensions 'have been given for a preferred embodiment of the lens, certain advantages result .from the arrangement .of surfaces without reference to the exact -or approximate relative 'dimensions of parts. Thus, for example, one of the principal advantages of the present reex reflecting lenses resides in the provision of a concave refracting surface which obviously requires less 4material than would otherwise be the caseand, more important, which reduces "the length of the path of an incident ray o'f light through vthe material tof the lens. This last is very important :and contributes greatly to the high percentage of Iincident light which is returned lwithina useful -zone 'adjacent the source.

While 'there is illustrated yand :described in vspecific detail 'a vpreferred lconstruction iof an improved catadioptric .reflex .reecting lens yand apparatus 'for `producing the same, it Wil1`be unvderstood that this has ibeen .done `merely to en- Iable those skilled in the 'art to `practice Ythe invention, the scope `of which is indicated by the appended claims.

What I vclaim `as my invention is:

l. A catadioptric `lens having a rear :surface provided 'with two `forwardly facing tetrahedral corners having a common side boundary,-each of said tetrahedral vcorners `composed of three concavely curved forwardly reflecting surfaces intersecti-ng 'at aicommonpointor apex, the axes of Symmetry ofl said tetrahedral corners being parallel, the frontface of said lens having a sinl gle concavely .curved front refracting surface whose axis is coplanar with and midway between the axesof symmetry of said tetrahedral corners,

`said corners and refracting surface being mutually optically cooperative to act as an autocollimating device.

2. A catadioptric lens having a rear surface provided with two forwardly facing tetrahedral corners having a common side boundary, each of said tetrahedral corners composed of three concavely curved forwardly reflecting surfaces intersecting at a common point or apex, the concavely curved reflecting surfaces' of each tetra- I rhedral corner being spherical surfaces, the axes of symmetry of said tetrahedral corners being parallel, the front face of said lens having a single concavely curved front refracting surface whose axis is coplanar with and midway between the axes of symmetry of said tetrahedral corners, said corners and refracting surface being mutual- 'ly optically cooperative to act as an autocollimatvingV device.

3. A catadioptric lens having a rear surface provided with two forwardly facing tetrahedral corners having a common side boundary, each of said tetrahedral corners composed of three concavely curved forwardly reflecting surfaces intersecting at a common point or apex, the concavely curved reflecting surfaces of each tetrahedral corner being spherical surfaces, and being tangent to planes which intersect at said apex and which are mutually normal to each other,

the axes of symmetry of said tetrahedral corners being parallel, the front face of said lens having a single concavely curved front refracting cavely curved forwardly reflecting surfaces intersecting at a common point or apex, the axes of symmetry of said tetrahedral corners being parallel, the front faceof said lens having a single concavely curved front refracting surface whose axis is coplanar with and midway between the vaxesrofsymmetry of said tetrahedral corners, said refracting surface being approximately hyperbolic, lsaid corners and refracting surface being mutually optically cooperative to act as an auto collimating device.

5. Afcatadioptric lens having a rear surface provided with two forwardly facing tetrahedral corners having a common side boundary, each of said tetrahedral corners composed of three concavely curved forwardly reflecting surfaces intersecting at a commonpoint or apex, the axes of symmetry of said tetrahedral corners being parallel, the front face of said lens having a single concavely curved front refracting surface whose axis is coplanar with and midway between the axes of symmetry of said tetrahedral corn ners, said refracting surface being approximately hyperbolic but modified therefrom to have a curvature of more rapidly increasing radius away from'its center, said corners and refracting sur- .v face being mutually optically cooperative to act as an autocollimating device.

6. Acatadioptric lens having a rear surface provided with two forwardly facing tetrahedral corners having a common side boundary, each of said tetrahedral corners composed of three concavely curved forwardly reecting surfaces intersecting at a common point or apex, the concavely curved reflecting surfaces of each tetrahedral corner being spherical surfaces, and being tangent to planes which intersectat said apex and which are mutually normal to each other, the axes of 'symmetry of said tetrahedral corners being parallel, the front face `of said lens having a single concavely curved front refracting surface whose axis is coplanar with and midway between the axes of symmetry of said-tetrahedral corners, said refracting surface being approximately hyperbolic but modified therefrom to have a curvature of more rapidly increasing radius away from its center, said corners and refracting surface being mutually optically cooperative to act as an autocollimating device.

7. A catadioptric lens having a, lrear surface provided with two forwardly facing tetrahedral corners having -a common side boundary, each of said tetrahedral corners composed of three concavely curved forwardly reflecting surfaces intersecting at a common point `or apex, the concavely curved reflecting surfaces of each tetrahedral corner being spherical surfaces and being tangent to planes which intersect at said apex and which are mutually normal'to each other, the axes of symmetry of said tetrahedral corners being parallel, the front face of said lens having a single concavely curved front refracting surface whose axis is coplanar with and midway between the axes of symmetry of said tetrahedral corners, said refracting surface being approximately hyperbolic but modified therefrom to have a curvature of more rapidly increasing radius away from the center, said corners and refracting surface being mutually optically cooperative to act as an autocollimating device, the radius of curvature of-'said spherical surfaces being several times greater than the average radius of curvature of said refracting surface.

y 8. A catadioptric lens having `a rear surface provided with two forwardly facing tetrahedral corners having a common side bound-ary, each of said tetrahedral corners composed of three concavely curved forwardly reflecting surfaces interseating at -a common point or apex, the concavely curved reflecting surfaces of each tetrahedral corner being spherical surfaces, having a radius of approximately 5.884 units, the axes of symmetry of said tetrahedral corners being parallel, the front face of said lens having a single concavely curved front refracting surface whose axis is coplanar with and midway between the axes of symmetry of said tetrahedral corners, said refracting surface being a surface of revolutions of a curve `whose coordinates in said units are substantially:

Slope of X l Y Normal where Athe X dimensions are taken along the ,axis of said surface and kthe Y dimensions are taken perpendicular to said X=dimensions, and :thelslope ofthe normal is taken as the angle between the axis and the line normal tothe curveat the points `designated. by the respective sets of vX and Y coordinates, saidcorners and .refracting surface being mutually optically cooperative to act as an autocollim-ating device.

9. A `ca'tadioptric `lens having `a rear surface provided with two forwardly facing 'tetrahedral corners having a common side boundary, each of said'tetrahedral-corners composed of three concavely curved forwardly reflecting surfaces intersecting at a common `point or apex, the axes of symmetry of said tetrahe'dral'corners being parallel, the front face of said lens having a single concavely curved front refractingsurface whose axis is coplanar with and midway between the axes of symmetry of said ltetrahedral corners, said refracting surface having a diameter greater than the distance between the yaxes of symmetry of said tetrahedral corners, said `corners and refracting surface being mutually optically cooperative to act as an autocollimating device.

10. A catadioptric lens having a rear surface provided `with two forwardly facing tetrahedral corners having a common side boundary, each of said tetrahedral cornersA composed of three concavely curved forwardly reflecting surfaces intersecting at a common point or apex, the axes of symmetry of said tetrahedral corners being parallel, the front 4face of said lens having a vsingle concavely curved front refracting surface whose axis is coplanar with'and midway between the axes v`of symmetry of said tetrahedral corners, said refracting surface `having a diameter greater than the minor diagonal ofthe assembly of said tetrahedral corners, said corners and refracting surface being mutually optically cooperative to act as an autocollimating device.

11. A catadioptric lens having `a rear surf-ace provided with two forwardly facing tetrahedral corners having a common side boundary, `each of said tetrahedral corners composed of three ooncavely curved forwardly reflecting surfaces intersecting at a common point or apex, the `concavely curved reflecting surfaces of each tetrahedral :cornerrbeing spherical surfaces, having a radius of approximately 5.884 units, and being tangent to planes which intersect at said apex and which are mutually normal to `each other, the axes of symmetry of said tetrahedral corners being parallel, the frontface of said lens having a single concavely curved front refracting surf-ace Whose axis is coplanar with and midway between the axes of symmetry of said tetrahedral corners, said refracting surface being a surface of revolutions of a curve whose coordinates in said units are substantially:

f Slope of X Normal 0.0000 0.0000 0 0 0. 0048 0. 0589 9 21 0. 0188 0. 1163 17 52 '0. 0388 0. 1674 24 30 0A 0638 0. 2155 29 35 '0. 0968 0. 2696 33 l5 0. 1328 0.3213 35 30 y0. 1734 0. 3750 38 20 0. 1984 0. 4063 39 30 0. 21,72 0. 4300 40 30' where the X Vdimensions are taken along the :axis of said surface and the Y dimensions are taken perpendicular to said X dimensions, vand the slope of the normal is taken as the angle between the axis and the line normal to the curve :at the points designated by the respective sets of X and Y coordinates, said corners and refracting surface being mutually optically cooperative to act as an autocollimating device.

ROY W. JOHNSON.

REFERENCES CITED The following ,references are of record in the file of this patent:

UNITED STATES PATENTS OTHER REFERENCES Van Lear, Reectors Used in Highway Signs and Warning Signals, article in Journal of Optical Soclety of America, vol. 30, October 1940, pps. 462-471, publ. by American Institute of Physics, `New York, New York. 

